The Role of the Zygomatic Arch in the Statics of the Skull and Its Adaptive Shape

Evolution of the temporal skull openings in land vertebrates: A hypothetical framework on the basis of biomechanics

The complex constructions of land vertebrate skulls have inspired a number of functional analyses. In the present study, we provide a basic view on skull biomechanics and offer a framework for more general observations using advanced modeling approaches in the future. We concentrate our discussion on the cranial openings in the temporal skull region and work out two major, feeding-related factors that largely influence the shape of the skull. We argue that (1) the place where the most forceful biting is conducted and (2) the handling of resisting food (sideward movements) constitute the formation and shaping of either one or two temporal arcades surrounding these openings. Diversity in temporal skull anatomy among amniotes can be explained by specific modulations of these factors with different amounts of acting forces which inevitably lead to deposition or reduction of bone material. For example, forceful anterior bite favors an infratemporal bar, whereas forceful posterior bite favors formation of an upper temporal arcade. Transverse forces (inertia and resistance of seized objects) as well as neck posture also influence the shaping of the temporal region. Considering their individual skull morphotypes, we finally provide hypotheses on the feeding adaptation in a variety of major tetrapod groups. We did not consider ligaments, internal bone structure, or cranial kinesis in our considerations. Involving those in quantitative tests of our hypotheses, such as finite element system synthesis, will provide a comprehensive picture on cranial mechanics and evolution in the future.

Functional reorganisation of the cranial skeleton during the cynodont-mammaliaform transition

Skeletal simplification occurred in multiple vertebrate clades over the last 500 million years, including the evolution from premammalian cynodonts to mammals. This transition is characterised by the loss and reduction of cranial bones, the emergence of a novel jaw joint, and the rearrangement of the jaw musculature. These modifications have long been hypothesised to increase skull strength and efficiency during feeding. Here, we combine digital reconstruction and biomechanical modelling to show that there is no evidence for an increase in cranial strength and biomechanical performance. Our analyses demonstrate the selective functional reorganisation of the cranial skeleton, leading to reduced stresses in the braincase and the skull roof but increased stresses in the zygomatic region through this transition. This cranial functional reorganisation, reduction in mechanical advantage, and overall miniaturisation in body size are linked with a dietary specialisation to insectivory, permitting the subsequent morphological and ecological diversification of the mammalian lineage.

Developmental constraint through negative pleiotropy in the zygomatic arch

BACKGROUND

Previous analysis suggested that the relative contribution of individual bones to regional skull lengths differ between inbred mouse strains. If the negative correlation of adjacent bone lengths is associated with genetic variation in a heterogeneous population, it would be an example of negative pleiotropy, which occurs when a genetic factor leads to opposite effects in two phenotypes. Confirming negative pleiotropy and determining its basis may reveal important information about the maintenance of overall skull integration and developmental constraint on skull morphology.

RESULTS

We identified negative correlations between the lengths of the frontal and parietal bones in the midline cranial vault as well as the zygomatic bone and zygomatic process of the maxilla, which contribute to the zygomatic arch. Through gene association mapping of a large heterogeneous population of Diversity Outbred (DO) mice, we identified a quantitative trait locus on chromosome 17 driving the antagonistic contribution of these two zygomatic arch bones to total zygomatic arch length. Candidate genes in this region were identified and real-time PCR of the maxillary processes of DO founder strain embryos indicated differences in the RNA expression levels for two of the candidate genes, Camkmt and Six2.

CONCLUSIONS

A genomic region underlying negative pleiotropy of two zygomatic arch bones was identified, which provides a mechanism for antagonism in component bone lengths while constraining overall zygomatic arch length. This type of mechanism may have led to variation in the contribution of individual bones to the zygomatic arch noted across mammals. Given that similar genetic and developmental mechanisms may underlie negative correlations in other parts of the skull, these results provide an important step toward understanding the developmental basis of evolutionary variation and constraint in skull morphology.

The Biomechanics of Zygomatic Arch Shape

Mammalian zygomatic arch shape is remarkably variable, ranging from nearly cylindrical to blade-like in cross section. Based on geometry, the arch can be hypothesized to be a sub-structural beam whose ability to resist deformation is related to cross sectional shape. We expect zygomatic arches with different cross sectional shapes to vary in the degree to which they resist local bending and torsion due to the contraction of the masseter muscle. A stiffer arch may lead to an increase in the relative proportion of applied muscle load being transmitted through the arch to other cranial regions, resulting in elevated cranial stress (and thus, strain). Here, we examine the mechanics of the zygomatic arch using a series of finite element modeling experiments in which the cross section of the arch of Pan troglodytes has been modified to conform to idealized shapes (cylindrical, elliptical, blade-like). We find that the shape of the zygomatic arch has local effects on stain that do not conform to beam theory. One exception is that possessing a blade-like arch leads to elevated strains at the postorbital zygomatic junction and just below the orbits. Furthermore, although modeling the arch as solid cortical bone did not have the effect of elevating strains in other parts of the face, as had been expected, it does have a small effect on stress associated with masseter contraction. These results are counterintuitive. Even though the arch has simple beam-like geometry, we fail to find a simple mechanical explanation for the diversity of arch shape. Anat Rec, 299:1734-1752, 2016. © 2016 Wiley Periodicals, Inc.

Review of In Vivo Bone Strain Studies and Finite Element Models of the Zygomatic Complex in Humans and Nonhuman Primates: Implications for Clinical Research and Practice

The craniofacial skeleton is often described in the clinical literature as being comprised of vertical bony pillars, which transmit forces from the toothrow to the neurocranium as axial compressive stresses, reinforced transversely by buttresses. Here, we review the literature on bony microarchitecture, in vivo bone strain, and finite-element modeling of the facial skeleton of humans and nonhuman primates to address questions regarding the structural and functional existence of facial pillars and buttresses. Available bone material properties data do not support the existence of pillars and buttresses in humans or Sapajus apella. Deformation regimes in the zygomatic complex emphasize bending and shear, therefore conceptualizing the zygomatic complex of humans or nonhuman primates as a pillar obscures its patterns of stress, strain, and deformation. Human fossil relatives and chimpanzees exhibit strain regimes corroborating the existence of a canine-frontal pillar, but the notion of a zygomatic pillar has no support. The emerging consensus on patterns of strain and deformation in finite element models (FEMs) of the human facial skeleton corroborates hypotheses in the clinical literature regarding zygomatic complex function, and provide new insights into patterns of failure of titanium and resorbable plates in experimental studies. It is suggested that the "pillar and buttress" model of human craniofacial skeleton function be replaced with FEMs that more accurately and precisely represent in vivo function, and which can serve as the basis for future research into implants used in restoration of occlusal function and fracture repair. Anat Rec, 299:1753-1778, 2016. © 2016 Wiley Periodicals, Inc.

Biomechanical implications of intraspecific shape variation in chimpanzee crania: moving toward an integration of geometric morphometrics and finite element analysis

In a broad range of evolutionary studies, an understanding of intraspecific variation is needed in order to contextualize and interpret the meaning of variation between species. However, mechanical analyses of primate crania using experimental or modeling methods typically encounter logistical constraints that force them to rely on data gathered from only one or a few individuals. This results in a lack of knowledge concerning the mechanical significance of intraspecific shape variation that limits our ability to infer the significance of interspecific differences. This study uses geometric morphometric methods (GM) and finite element analysis (FEA) to examine the biomechanical implications of shape variation in chimpanzee crania, thereby providing a comparative context in which to interpret shape-related mechanical variation between hominin species. Six finite element models (FEMs) of chimpanzee crania were constructed from CT scans following shape-space Principal Component Analysis (PCA) of a matrix of 709 Procrustes coordinates (digitized onto 21 specimens) to identify the individuals at the extremes of the first three principal components. The FEMs were assigned the material properties of bone and were loaded and constrained to simulate maximal bites on the P(3) and M(2) . Resulting strains indicate that intraspecific cranial variation in morphology is associated with quantitatively high levels of variation in strain magnitudes, but qualitatively little variation in the distribution of strain concentrations. Thus, interspecific comparisons should include considerations of the spatial patterning of strains rather than focus only on their magnitudes.

Development and three-dimensional morphology of the zygomaticotemporal suture in primate skulls

Cranial sutures are an essential part of the growing skull, allowing bones to increase in size during growth, with their morphology widely believed to be dictated by the forces and displacements that they experience. The zygomaticotemporal suture in primates is located in the relatively weak zygomatic arch, and externally it appears a very simple connection. However, large forces are almost certainly transmitted across this suture, suggesting that it requires some level of stability while also allowing controlled movements under high loading. Here we examine the 2- and 3-dimensional (3D) morphology of the zygomaticotemporal suture in an ontogenetic series of Macaca fascicularis skulls. High resolution microcomputed tomography data sets were examined, and virtual and physical 3D replicas were created to assess both structure and general stability. The zygomaticotemporal suture is much more complex than its external appearance suggests, with interlocking facets between the adjacent zygomatic and temporal bones. It appears as if some movement is permitted across the suture in younger animals, but as they approach adulthood the complexity of the suture's interlocking bone facets reaches a level where these movements become minimal.

Predicting skull loading: applying multibody dynamics analysis to a macaque skull

Evaluating stress and strain fields in anatomical structures is a way to test hypotheses that relate specific features of facial and skeletal morphology to mechanical loading. Engineering techniques such as finite element analysis are now commonly used to calculate stress and strain fields, but if we are to fully accept these methods we must be confident that the applied loading regimens are reasonable. Multibody dynamics analysis (MDA) is a relatively new three dimensional computer modeling technique that can be used to apply varying muscle forces to predict joint and bite forces during static and dynamic motions. The method ensures that equilibrium of the structure is maintained at all times, even for complex statically indeterminate problems, eliminating nonphysiological constraint conditions often seen with other approaches. This study describes the novel use of MDA to investigate the influence of different muscle representations on a macaque skull model (Macaca fascicularis), where muscle groups were represented by either a single, multiple, or wrapped muscle fibers. The impact of varying muscle representation on stress fields was assessed through additional finite element simulations. The MDA models highlighted that muscle forces varied with gape and that forces within individual muscle groups also varied; for example, the anterior strands of the superficial masseter were loaded to a greater extent than the posterior strands. The direction of the muscle force was altered when temporalis muscle wrapping was modeled, and was coupled with compressive contact forces applied to the frontal, parietal and temporal bones of the cranium during biting.

Assessing mechanical function of the zygomatic region in macaques: validation and sensitivity testing of finite element models

Crucial to the interpretation of the results of any finite element analysis of a skeletal system is a test of the validity of the results and an assessment of the sensitivity of the model parameters. We have therefore developed finite element models of two crania of Macaca fascicularis and investigated their sensitivity to variations in bone material properties, the zygomatico-temporal suture and the loading regimen applied to the zygomatic arch. Maximum principal strains were validated against data derived from ex vivo strain gauge experiments using non-physiological loads applied to the macaque zygomatic arch. Elastic properties of the zygomatic arch bone and the zygomatico-temporal suture obtained by nanoindentation resulted in a high degree of congruence between experimental and simulated strains. The findings also indicated that the presence of a zygomatico-temporal suture in the model produced strains more similar to experimental values than a completely separated or fused arch. Strains were distinctly higher when the load was applied through the modelled superficial masseter compared with loading an array of nodes on the arch. This study demonstrates the importance of the accurate selection of the material properties involved in predicting strains in a finite element model. Furthermore, our findings strongly highlight the influence of the presence of craniofacial sutures on strains experienced in the face. This has implications when investigating craniofacial growth and masticatory function but should generally be taken into account in functional analyses of the craniofacial system of both extant and extinct species.

Techniques for Modeling Muscle-induced Forces in Finite Element Models of Skeletal Structures

This work introduces two mechanics-based approaches to modeling muscle forces exerted on curvilinear bone structures and compares the results with two traditional ad hoc methods of muscle loading. These new models use a combination of tensile, tangential, and normal traction loads to account for muscle fibers wrapped around curved bone surfaces. A computer program was written to interface with a commercial finite element analysis tool to automatically apply traction loads to surface faces of elements in muscle attachment regions according to the various muscle modeling methods. We modeled a highly complex skeletal structure, the skull of a Jamaican fruit bat (Artibeus jamaicensis), to compare the four muscle-loading methods. While reasonable qualitative agreement was found in the states of stress of the skull between the four muscle load modeling methods, there were substantial quantitative differences predicted in the stress states in some high stressed regions of the skull. Furthermore, our mechanics-based models required significantly less total applied muscle force to generate a bite-point reaction force identical to those produced by the ad hoc muscle loading models. Although the methods are not validated by in vivo data, we submit that muscle-load modeling methods that account for the underlying physics of muscle wrapping on curved bone surfaces are likely to provide more realistic results than ad hoc approaches that do not. We also note that, due to the geometric complexity of many bone structures--such as the skull analyzed here--load transmission paths are difficult to conceptualize a priori. Consequently, it is difficult to predict spatially where the results of finite element analyses are likely to be compromised by using ad hoc muscle modeling methods. For these reasons, it is recommended that a mechanics-based method be adopted for determination of the proper traction loads to be applied to skeletal structures due to muscular activity.

Functional shape of the skull in vertebrates: Which forces determine skull morphology in lower primates and ancestral synapsids?

In order to determine the extent to which the shape of the synapsid skull is adapted for resisting the mechanical loads to which it is subjected, block- or simple plate-shaped finite-element models were constructed and loaded with external muscle and bite forces in locations estimated to resemble points of application of these forces. These 2D or 3D finite-element models were iteratively loaded and modified by removing elements that experience only low stresses, and the resulting morphologies of the models were compared with fossil skulls of synapsids and the skulls of extant mammals. The results suggest that the stress flows in these unspecific models are very similar to the arrangement of bone material in real skulls. Morphological differences between taxa depend on a few a priori conditions: length and position of the tooth rows in relation to the braincase, arrangement of muscles, position of the orbits, and position of the nasal opening. Given these initial conditions, finite-element analysis consistently reveals the close similarity between stress flows and real skulls. The major difference between mammal-like reptiles and primates is the size of the braincase. This difference accounts for most of the morphological divergence. The postorbital bar seems to be a constructional element of the skull, rather than a means to protect the eyes. The skull shapes of higher primates are determined mainly by masticatory forces and less by external forces acting on the head. This study demonstrates the utility of finite-element modeling for testing hypotheses regarding relationships between form and function in vertebrate skulls.

Finite element analysis in functional morphology

This article reviews the fundamental principles of the finite element method and the three basic steps (model creation, solution, and validation and interpretation) involved in using it to examine structural mechanics. Validation is a critical step in the analysis, without which researchers cannot evaluate the extent to which the model represents or is relevant to the real biological condition. We discuss the method's considerable potential as a tool to test biomechanical hypotheses, and major hurdles involved in doing so reliably, from the perspective of researchers interested in functional morphology and paleontology. We conclude with a case study to illustrate how researchers deal with many of the factors and assumptions involved in finite element analysis.

A biomechanical approach to craniofacial shape in primates, using FESA

The head of a land-living vertebrate is exposed to the forces of acceleration, in particular the permanent earth acceleration (= gravity) and the muscle-generated bite and chewing forces. In mammals, at least, the latter seem to play the dominant role. Bite forces are applied to the teeth and close the circle of forces by passing through the facial skeleton to the insertions of the mandibular adductors. With the aid of three-dimensional Finite Element Systems Analysis (FESA), the stress flows in homogenous bodies are investigated, whereby the braincase, the orbits and the nasal channel are taken as preconditions. The muscle insertions are varied systematically. The resulting stress flows in all cases turn out to be very similar to the bony structures of a skull. Little or not stressed parts of the available homogenous body indicate the external surface or hollow spaces (= sinuses) inside the skull. The possible applications of forces (i.e., the forms and positions of the dental arcade in relation to the braincase) determine the pathways along which the forces are transmitted. It seems that the factors mentioned above as preconditions represent the selective pressures exerted by the lifestyle of the animal and its environment (= ecological conditions). The results that can be obtained by our deductive approach in comparison to inductive, experimental procedures are discussed briefly.